Theorems · Theorem · category theory

CategoryTheory.Functor.homEquivOfIsRightKanExtension_apply_app

∀ {C : Type u_1} {H : Type u_3} {D : Type u_4} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_3, u_3} H] [inst_2 : CategoryTheory.Category.{v_4, u_4} D]
  (F' : CategoryTheory.Functor D H) {L : CategoryTheory.Functor C D} {F : CategoryTheory.Functor C H}
  (α : L.comp F' ⟶ F) [inst_3 : F'.IsRightKanExtension α] (G : CategoryTheory.Functor D H) (β : G ⟶ F') (X : C),
  ((F'.homEquivOfIsRightKanExtension α G) β).app X = CategoryTheory.CategoryStruct.comp (β.app (L.obj X)) (α.app X)

Defined in

Mathlib.CategoryTheory.Functor.KanExtension.Basic

Cited by

0 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.IsRightKanExtension